The right-hander out of the University of Connecticut was drafted No. 19 overall, a ways away from some projections that had him being selected in the first five or 10 picks.
And even if it meant being taken by his favorite team's enemy, Barnes said he wasn't disappointed that he fell to No. 19.
"No, not at all," he said. "Being drafted anywhere in the first round is obviously very respectable. ... As much as I've always been a Yankees fan, I've always respected the Red Sox. They have a great organization. They're a great team. They develop their players well."
While it could be easy for Barnes to focus on nothing else but becoming a professional ballplayer, the lanky pitcher is in South Carolina this weekend after UConn defeated Clemson in NCAA regional play. A win would put the Huskies in the College World Series.
"The Draft actually took place during our regional championship game against Clemson, which was kind of neat," Barnes said. "As much as I would have loved to be with my family and friends, it was great to be with my teammates and experience not only the Draft with them, but winning a regional and going to the Super Regional.
"This week, we're just practicing really hard and hopefully going into USC and take two out of three from the Gamecocks and head to Omaha."
A power pitcher, Barnes can dial his fastball up to 97 mph, but the development of his offspeed pitches has turned him into much more than just a flamethrower.
"Coming out of high school, my mechanics were easy and fluent, so that allowed me to throw the ball hard, but there were a couple minor adjustments," he said. "I kind of grew as a person, I grew as a player. I matured a lot. [I] kind of grew into my body, put on some weight. I've become a lot stronger since high school, because in high school, in my conference, if you threw 90 mph, you're going to be a dominant pitcher."
Barnes is 11-4 with a 1.62 ERA and 111 strikeouts over 116 2/3 innings for the Huskies this season. But he wasn't the only UConn player to be drafted, and not even the first.
Outfielder George Springer was taken by the Astros No. 11 overall, but Barnes said there's nothing but friendly competition between them.
"Me and George are really good friends," he said. "We always live together on the road, we live in the same building back on campus, we played together in college and in the summer. That's the great thing about where our friendship is at. Our friendship isn't based on baseball."
While Red Sox general manager Theo Epstein had personally seen Barnes play several times at UConn, the pitcher said he would refrain from talking to the club about signing a contract until his college season is over.
"Once the season is over with UConn is when I'll sit down with my parents and talk about it," he said. "We'll talk to the Red Sox and see what they want to do."
Jason Mastrodonato is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.